X-inner automorphisms of semi-commutative quantum algebras

Many important quantum algebras such as quantum symplectic space, quantum E uclidean space, quantum matrices, q-analogs of the Heisenberg algebra, and the quantum Weyl algebra are semi-commutative. In addition, enveloping alge bras U(L+) of even Lie color algebras are also semi-commutative. In this pa per, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras. The theorems and examples in our paper show that for alg ebras R of this type, the non-identity X-inner automorphisms of R tend to h ave infinite order. Thus if G is a finite group of automorphisms of R, then the action of G will be X-outer and this immediately gives useful informat ion about crossed products R *(t) G. (C) 1999 Academic Press.